1. Field of the Invention
This invention relates to waveguides, and more particularly, a technique for maximizing the efficiency of an array of waveguides.
2. Description of the Prior Art
Waveguide arrays are used in a wide variety of applications such as phased array antennas and optical star couplers. FIG. 1 shows one such waveguide array comprising three waveguides 101-103 directed into the x-z plane as shown. The waveguides are separated by a distance "a" between the central axis of adjacent waveguides, as shown. A figure of merit for such a waveguide array is the radiated power density P(.theta.) as a function of .theta., the angle from the z-axis. This is measured by exciting one of the waveguides in the array, i.e. waveguide 102, with the fundamental input mode of the waveguide, and then measuring the radiated pattern. Ideally, it is desired to produce a uniform power distribution as shown in ideal response 202 of FIG. 2, where (.gamma.) is specified by the well-known equation EQU [a] sin (.gamma.)=.lambda./2, (1)
where .lambda. is the wavelength of the radiated power in the medium occupying the positive z plane of FIG. 1. The angular distance from -.gamma. to .gamma. is known as the central Brillouin zone. In practice, it is impossible to produce ideal results. An exemplary response from an actual array would look more like typical actual response 201 of FIG. 2. The efficiency of the array, N(.theta.), when one waveguide is excited, is the ratio of the actual response divided by the ideal response, for all .theta. such that -.gamma..ltoreq..theta..ltoreq..gamma.. Of course, this neglects waveguide attenuation and reflection losses. With this background, the operation of phased array antennas is discussed below.
The operation of a prior art phased array antenna can be described as follows. The input to each waveguide of FIG. 1 is excited with the fundamental mode of the input waveguides. The signal supplied to each waveguide is initially uncoupled from the signals supplied to the other waveguides and at a separate phase, such that a constant phase difference .phi. is produced between adjacent waveguides. For example, in FIG. 1, waveguide 101 could be excited with a signal at zero phase, waveguide 102 with the same signal, at 5.degree. phase, waveguide 103 with the same signal at 10.degree. phase, and so forth for the remaining waveguides in the array (not shown). This would imply a phase difference of 5.degree. between any two adjacent waveguides. The input wave produced by this excitation is known as the fundamental Bloch mode, or linear phase progression excitation. When the input excitation is the fundamental Bloch mode, the output from the waveguide array, part of which is illustrated in FIG. 3, will be a series of plane waves, e.g., at directions .theta..sub.0,.theta..sub.1 and .theta..sub.2, each in a different direction, where the direction of the m.sup.th plane wave is specified by: ##EQU1## and the wavefront radiated in the direction of .theta..sub.0 is the only wavefront in the central Brillouin zone and is specified by the relationship .phi.=kasin(.theta..sub.0), m=.+-.1, .+-.2 . . . , and k=2.pi./.lambda. in the medium occupying the positive z plane. The direction of .theta..sub.0, and consequently of all the other plane waves emanating from the waveguide array, can be adjusted by adjusting the phase difference .phi. between the inputs to adjacent elements. It can be shown that the fraction of the power radiated at direction .theta..sub.0 when the inputs are excited in a linear phase progression is N(.theta.), defined previously herein for the case of excitation of only one of the waveguides with the fundamental mode.
The relationship between the response of the array to excitation of a single waveguide with the fundamental mode, and the response of the array to the fundamental Bloch mode can be further understood by way of example. Suppose in a Bloch mode excitation .phi. is adjusted according to .phi.=kasin .theta..sub.0 such that .theta..sub.0 is 5.degree..
The power radiated at 5.degree. divided by the total input power=N(5.degree.). However, if only one waveguide is excited, and a response similar to response 201 of FIG. 2 is produced in the Brillouin zone, then at .theta.=5.degree., P(.theta.).sub.actual /P(.theta.).sub.ideal =N(5.degree.).
The fractional radiated power outside the central Brillouin zone of FIG. 2, or equivalently, the percentage of the power radiated in directions other than .theta..sub.0 in FIG. 3, should be minimized in order to maximize performance. In a phased array radar antenna, for example, false detection could result from the power radiated in directions other than then .theta..sub.0. It can be shown that the wavefront in the direction .theta..sub.1 of FIG. 3 comprises most of the unwanted power. Thus, it is a goal of many prior art waveguide arrays, and of this invention, to eliminate as much as possible of the power radiated in the .theta..sub.1 direction, and thus provide a high efficiency waveguide array.
Prior art waveguide arrays have attempted to attain the goal stated above in several ways. One such prior art array is described in N. Amitay et al., Theory and Analysis of Phased Array Antennas, New York, Wiley Publisher, 1972, at pp. 10-14. The array achieves the goal by setting the spacing between the waveguide centers equal to .lambda./2 or less. This forces .gamma. to be at least 90.degree., and thus the central order Brillouin zone occupies the entire real space in the positive z plane of FIG. 1. This method, however, makes it difficult to aim the beam in a narrow desired direction, even with a large number of waveguides. The problem that remains in the prior art is to provide a waveguide array which, when excited with a Bloch mode, can confine a large portion of its radiated power to the direction .theta..sub.0 without using a large number of waveguides. Equivalently, the problem is to provide a waveguide array such that when one waveguide is excited with the fundamental mode, a large portion of the radiated power will be uniformly distributed over the central Brillouin zone.